Progressive power ophthalmic lens having a plurality of viewing zone with discontinuous power variations therebetween

ABSTRACT

A progressive power ophthalmic lens is described on which one refractive surface is formed to provide zones at the top and bottom of the refractive surface having constant dioptric focal powers. The two zones having constant dioptric focal power are of different radii of curvature such that a near viewing zone is located at the bottom and a distance viewing zone is located at the top of the refractive surface. Between these two constant dioptric focal power zones lies an intermediate zone having progressive dioptric focal power within a range centered between the dioptric focal powers of the upper and lower zones. There is a downwardly positive discontinuity in the dioptric focal power at the boundary between at least one of the constant dioptric focal power zones and the intermediate zone having progressive dioptric focal power. This power discontinuity lowers the rate of addition of dioptric focal power through the progressive power intermediate zone. This decreased rate of addition limits the amount of astigmatism and distortion which are introduced into the peripheral zones of the refractive surface. The discontinuities are rendered invisible on the surface so that a smooth surface is provided on the progressive power ophthalmic lens and the refractive surface areas near the periphery of the lens are formed from sections of a figure of revolution.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a continuation-in-part of co-pending patentapplication Ser. No. 389,043 filed on Aug. 16, 1973, now abandoned, andfurther relates to co-pending applications Ser. No. 389,942 entitled"Progressive Power Ophthalmic Lens" and Ser. No. 389,044 entitled"Multifocal Lens", both co-pending applications being filed on Aug. 16,1973 and both now abandoned.

BACKGROUND OF THE INVENTION

This invention is related to ophthalmic lenses in general and is moreparticularly concerned with novel progressive power and multifocalophthalmic lenses in which the distortion is either so controlled that awearer perceives vertical lines as vertical throughout most of theviewing area of the ophthalmic lens or the degree of distortion isseverely diminished.

The human eye is a sensitive yet relatively simple organ. It contains alens on the outer surface for receiving light from various objects inthe field of view of the eye. A retina is positioned behind the lens toserve as a viewing screen for those rays focused by the lens onto theretina. A series of muscles surround the lens and act upon the lens toincrease or decrease its curvature and focal length in order to focusupon objects which are either near to the eye or at a distance. When thenormal eye views relatively distant objects, the lens and the musclesare in a relaxed position. In this position, the ideal lens has theproper curvature on its surface to focus the distant object on theretina. Upon the observance of objects at close range, the eye musclesact on the lens to increase its curvature and decrease the focal lengthof the lens sufficiently to focus the image of the near object onto theretina. This ability of the eye to adjust itself for varying objectdistances is commonly known as "accommodation". As the age of a humanbeing increases, his power of accommodation generally decreases. Thisresults from the fact the eye muscles become stiff and weak. Forexample, a child can normally change the focal power of his eye by atleast 14 diopters. In a middle age person, the power of accomodation isoften reduced to about 3 diopters, and in old age, the power ofaccomodation may disappear entirely.

For a long time, scientists and optical engineers have attempted to findsolutions to this problem of decreasing accomodation with age. Probablythe most common means which has been devised for treating this conditionis to construct the corrective ophthalmic lens utilized by the personwith decreased accomodation with a plurality of spherical surfaces.These are commonly known as bifocal and trifocal lenses depending uponwhether the lens in question contains two or three spherical portions.In the bifocal lens, two separate segments of different dioptric focalpowers are provided. The power of one segment is such that visionthrough it permits focusing on nearby objects such as reading matterwhile the other segment corrects the vision for viewing distant objects.In a trifocal ophthalmic lens a third spherical segment is interposedbetween the previously mentioned two segments to provide a measure ofclear vision to the wearer intermediate between the dioptric focalpowers of the distance and reading segments of the lens. The othersurface of the mutlifocal ophthalmic lens is then provided with either aspherical or toric surface designed specifically to adapt the multifocallens to the particular ophthalmic prescription of the wearer.

Certain major difficulties are, however, encountered by the users ofmutlifocal ophthalmic lenses. Firstly, there is a line of sharpdemarcation optically between the various segments of the multifocallens. When the line of sight scans across this dividing line, a "jump"usually occurs in the image perceived by the wearer. It is difficult forthe wearer to become accustomed to this sensation and to make allowancesfor it in normal life. Secondly, persons having severely reducedaccomodation are unable to focus clearly on objects lying at distancesbetween those distances at which the various segments are designed tofocus. Thirdly, particularly in younger people having reducedaccomodation powers, it is often difficult to convince some individualsthat they require multifocal ophthalmic lenses for vision purposes. Thisis generally attributed to the fact that decreased accomodation isassociated with oncoming age. The standard multifocal lens has adistinct line of demarcation between the various segments which isreadily apparent to people in the vicinity of the wearer. Therefore, aswell as the optical problems which exist with multifocal ophthalmiclenses, also certain cosmetic problems exist.

The obvious general solution to these problems is to place anintermediate viewing zone between the distance viewing zone and thereading zone which progresses in dioptric focal power from that of thedistance viewing portion to that of the reading portion. By attemptingthis solution, an ophthalmic lens is provided in which both the opticaland cosmetic problems may be solved in that there are neither lines ofoptical jump between distinct segments nor are there cosmeticallyobvious lines between the various segments. Furthermore, allintermediate focal powers between the distance and reading portions areprovided such that the wearer is able to perceive objects at anydistance clearly through a portion of this intermediate zone. Such alens is known commonly as a progressive power ophthalmic lens. Anexcellent survey of such lenses was provided by A. G. Bennett in theOctober and November 1970, and February and March 1971 issues of TheOptician. In this work, the various attempts are discussed which havebeen made to provide such progressive power ophthalmic lenses by variousscientists and optical engineers over approximately the last 70 years.

All progressive power lenses of the prior art have suffered from atleast one common failing. As a necessary concomitant of an asphericalsurface such as is found in the progressive power lenses, a certainamount of astigmatism and distortion is inherently found in therefractive surface, particularly in the peripheral portions of thetransitional zone. The distortion causes a swimming or rocking effectwhen the wearer's head is moved within the visual environment. Thiseffect has served to cause many wearers of such ophthalmic lenses tobecome nauseated and has definitely prevented the wide acceptance ofthis type of eyewear. Furthermore, the astigmatism causes blurring ofvision through the affected areas of the lens. This effect is, ofcourse, objectionable as well.

Distortion occurs whenever astigmatism is present in the refractingsurface. Thus distortion, like astigmatism, is an inevitable consequenceof progressive power refractive ophthalmic surfaces. Many attempts havebeen made in the prior art to minimize the effect of the astigmatism.Generally, these attempts have centered on the scheme by which therefractive surface having the aspherical curvature is generated. Themore successful attempts have resulted in spreading the astigmatism overa large portion of the refractive surface. This, at a minimum, reducedthe size of the reading zone below that which allows the wearer to readstandard material without turning his head.

SUMMARY OF THE INVENTION

Accordingly, it is an object of the present invention to provide a newand novel progressive power ophthalmic lens in which the swimming orrocking of images viewed through the peripheral portions of the lens iseliminated.

Another object of the invention is to provide such a progressive powerophthalmic lens in which the reading portion having spherical curvatureis conveniently large so that normal reading habits may be maintained bywearers of the lenses.

A still further object of the invention is to provide such a progressivepower lens in which the deleterious effects of the distortion areminimized.

It is a further object of the invention to provide such a progressivepower ophthalmic lens having a high degree of freedom in designparameters such that the design may be adapted to a wide variety ofdifferent specific ophthalmic configurations.

A still further object of the invention is to provide such a novelprogressive power ophthalmic lens which is relatively simple inconstruction and capable of large quantity manufacture.

Briefly, the invention in its broadest aspect comprises an ophthalmiclens having a refractive surface thereon. A smooth, unbroken principalmeridional curve having continuously varying slope lies along a firstrefractive surface veiwing zone in a generally vertical direction anddivides the refractive surface viewing zone into two similar lateralportions. The curvature of the principal meridional curve variesprogressively from point to point therealong to provide a predetermineddioptric focal power at each such point according to a predeterminedlaw. The dioptric focal power increases generally from top to bottom ofthe progressive power lens along the principal meridional curve. Therefractive surface is further characterized by having cross curvesdefined thereon by planes perpendicular to the principal meridionalcurve, the curvatures of the cross curves at their points ofintersection with the principal meridional curve being respectivelyequal to the curvature of the principal meridional curve at the pointsof intersection. At least two viewing zones in vertical juxtapositionare defined on the refractive surface by the predetermined law and havea boundary therebetween. The first one of the viewing zones hascontinuously progressive dioptric focal power varying over a range froma first dioptric focal power at the top of the viewing zone to a second,higher dioptric focal power at the bottom of the first viewing zone. Thesecond one of the viewing zone has a constant dioptric focal power atthe bottom of the first viewing zone. The second one of the viewing zonehas a constant dioptric focal power therethrough. There is a downwardlypositive discontinuity in the predetermined law at the boundary betweenthe two viewing zones.

The instant application is distinguished from above-identified relatedapplications Ser. Nos. 389,042 and 398,044 at least by the feature thatthe instant application is directed inter alia to lens structure thatdoes have power discontinuities.

Further objects, advantages, and features of the invention will beapparent in the arrangement and construction of the constituent parts,in detail, as set forth in the following specification taken togetherwith accompanying drawing.

DESCRIPTION OF THE DRAWING

In the drawing,

FIG. 1 is an isometric view of a progressive power ophthalmic lensaccording to the invention;

FIG. 2 is a vertical sectional view of the progressive power ophthalmiclens of FIG. 1 taken along the principal vertical meridional curve;

FIG. 3 is a front elevation view of a progressive power ophthalmic lensshowing the various viewing zones and the associated power law;

FIG. 4 is schematic illustration of the technique for generating theprogressive power surface of FIG. 3;

FIG. 5 is a front elevation view of a progressive power ophthalmic lenswhose intermediate and near vision portions are divided laterally into aplurality of areas, the outermost of which are totally corrected forskew distortion;

FIGS. 6 through 11 are illustrative diagrams of the images of a squaregrid as viewed through various embodiments of the progressive powerophthalmic lens of the present invention;

FIG. 12 is a schematic diagram of a symmetrical progressive power lensaccording to the invention which has been rotated 10 degrees from thevertical to accomodate for decreasing interpupilary spacing when viewingcloser objects;

FIG. 13 is a schematic diagram of a matched set of progressive powerlens which compensate for the 10° rotation required.

FIGS. 14A through 14C are exemplary power law diagrams illustrating theuse of discontinuities;

FIG. 15 is a table illustrating the effect of power law discontinuities;

FIG. 16 is an illustrative diagram of the image of a square grid asviewed through a progressive power lens having no finite powerdiscontinuities at the boundaries of the intermediate viewing zone;

FIG. 17 is an illustrative diagram of the image of a square grid asviewed through a progressive power lens having finite powerdiscontinuities at the boundaries of the intermediate viewing zone;

FIG. 18 is a front elevation view of a progressive power ophthalmic lensin which finite power discontinuities at the boundaries of theintermediate viewing zone are blended to render them invisible;

FIG. 19 is a front elevation view of a multifocal ophthalmic lensaccording to the present invention whose intermediate and near visionsegments are divided laterally into a plurality of areas, the outermostof which exhibits only normal distortion, the lens being susceptible toa manufacturing process for blending out the segment dividing lines;

FIG. 20 is an illustrative diagram of the image of a square grid asviewed through a multifocal lens of the present invention;

FIG. 21 is a front elevational view of the multifocal lens used for FIG.20 in which the surface discontinuities at the boundaries betweensegments are blended to render them invisible.

FIG. 22 is a perspective elevation view of a progressive powerophthalmic lens on which the surfaces of the lateral peripheries areillustrated as being constructed in accordance with portions of a figureor surface of revolution;

FIG. 23 is a front elevation view of a lens mold or block showing theconcave surface of the mold or block;

FIG. 24 is an exemplary embodiment of a surface shape which may beprovided upon a slumping block used to form a mold for casting a lensaccording to principles of the present invention;

FIG. 25 is a diagram of a square grid as viewed through a lens of thepresent invention which, when compared with FIG. 17, illustrates acorrection of skew distortion and smoothening according to theinvention; and

FIG. 26 is an exemplary embodiment of a surface shape which may beprovided upon a slumping block used to produce a mold for casting a lensof the type depicted in FIG. 25.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In referring to the various figures of the drawing herebelow, likereference numerals will be utilized to refer to identical parts.

Referring initially to FIG. 1, there is shown a progressive powerophthalmic lens 10. The lens is constructed of an optical materialhaving a uniform refractive index such as optical quality glass or oneof the well-known optical quality plastic materials such as CR-39 (allyldiglycol carbonate), Lexan (polycarbonate), or methyl methacrylate.Progressive power is accomplished in the lens 10 by forming one of thetwo surfaces into an appropriate aspherical form. Generally, the surfaceutilized for forming the aspherical surface is the front surface of thelens, i.e., that surface of the lens which is of convex form. However,the principal reason for this choice is that conventional grinding andpolishing machinery located at various dispensing branches is configuredto apply the spherical or toroidal surface dictated by the intendedwearer's particular ophthalmic prescription on the rear surface of theophthalmic lens. Therefore, in this introductory portion as well as theremainder of the following description of the invention, the asphericalsurface will be shown and described as being present as the frontsurface of the ophthalmic lens. Although it is not intended that theinvention be so limited.

For purposes of this description, the progressive power ophthalmic lens10 is fixed in space in approximately the orientation in which it is tobe worn by the patient. More particularly, as shown in FIG. 1, the lens10 is oriented such that the aspherical surface is tangent to a firstvertically oriented plane 12 at the geometrical center 14 of the lensblank 10. A second vertically oriented plane 16, perpendicular to thefirst vertically oriented plane 12, also intersects the ophthalmic lens10 at point 14 and divides the lens 10 into two symmetrical halves. Theplane 16 is generally referred to as the principal vertical meridionalplane. The principal vertical meridional plane 16 intersects theaspherical surface of the lens 10 in a plane curve 18 called theprincipal meridional line or curve.

If the progressive power ophthalmic lens 10 is to work properly, theprincipal meridional line 18 must be continuous and it must havecontinuously varying slope. The first condition ensures that there willbe no visible discontinuity in the surface of the lens at the principalmeridional line. The second condition ensures that there will be noimage jump as the wearer's line of sight moves vertically along theprincipal meridional line. In order to provide for progressiveaccommodation in the lens, the curvature of the principal meridionalline 18 increases in a downwardly positive manner from a far visionvalue near the top of the lens to a near vision value near the bottom.Depending upon the requirements of the particular design, the amount ofdioptric focal power addition between the upper and lower limits(commonly known as "add") may vary appreciably. The absolute amount ofdioptric focal power addition is variable and is dependent upon theretained powers of accommodation on the part of the wearer. The rate ofaddition along the principal meridional line 18 is also variable. Inother words, the transitional dioptric focal power may be introducedover a very short portion of the principal meridional line or it may beintroduced over esentially the entire length of the principal meridionalline.

In general, it is preferred that the astigmatism along the principalmeridional line 18 be essentially zero. Astigmatism is generally definedwith respect to a point on a refractive surface and two perpendicularlydisposed planes intersecting thereat and passing through the normal tothe refractive surface at the point, the first or sagittal planeestablished by the minimum radius of curvature of the refractive surfaceand the second or meridional plane established by the maximum radius ofcurvature of the refractive surface at the point, then the magnitude ofthe astigmatism is taken as the difference between the dioptric focalpower of the refractive surface in the first plane and the dioptricfocal power of the lens in the second plane. The amount of astigmatismat any point on the refractive surface of the lens is measured by thedifference in the dioptric focal power between the sagittal plane andthe meridional plane of the point. The curvatures of the refractivesurface at any point in the sagittal and meridional planes are commonlyknown as the principal curvatures at that point. This astigmatism couldbe called intrinsic in order to distinguish it from that astigmatismthat arises when a spherical surface is illuminated by rays of lightstriking the surface at oblique angles of incidence.

Along the vertical principal meridional curve 18, the refractive surfaceis umbilic, i.e., there is only a single radius of curvature at anygiven point. If r is the radius of curvature of the principal meridionalline at Q, and n is the index of refraction of the lens material, then,if the principal curvatures of the surface at Q are equal, the dioptricfocal power P_(O) at this point is given by

    P.sub.O = n-1/r

Referring now to FIG. 2, there is shown a sectional view of the lens 10taken along the principal vertical meridional plane 16. The locus of thecenters of curvatures of the principal meridional line 18 comprises acontinuous plane curve 22 called the evolute of the principal meridionalline which is also located within the principal meridional plane. Toeach point Q of the principal meridional line 18 there corresponds apoint q on the evolute. The radius vector 20 connecting any two suchpoints is perpendicular to the principal meridional line 18 at Q andtangent to the evolute curve 22 at q.

A typical and particularly useful form of progressive power ophthalmiclens incorporating the foregoing principles is shown in FIG. 3. The lens30 consists of three vertically disposed viewing zones 32, 36, and 34respectively. Here again, a principal meridional line 18 bisects thelens in a generally vertical direction. The uppermost viewing zone ofthe lens 32 is formed with a constant dioptric focal power whichaccommodates vision to distant objects, i.e., the surface in viewingzone 32 is spherical. The lowermost viewing zone 34 of the lens isagains of constant dioptric focal power and accommodates the vision tonearby objects. Interposed between viewing zones 32 and 34 is anintermediate viewing zone 36 having progressive power which provides agradual optical transition between viewing zones 32 and 34. In otherwords, the dioptric focal power varies continuously over a range from afirst dioptric focal power at the top of the intermediate viewing zoneto a second, higher dioptric focal power at the bottom of the zone. Thisis consistent with the requirement that the dioptric focal powerincrease generally from top to bottom of the progressive powerophthalmic lens along the principal meridional curve.

The height of the intermediate portion of the lens along the meridionalcurve is identified as h. The graph at the right of FIG. 3 is known asthe "power law" of the lens 30. The power law in this instance consistsof three linear portions 38, 40, and 42 which are respectivelyassociated with the lens viewing zones 32, 34 and 36 respectively alongthe principal meridional line B. The portion 38 represents the constantdioptric focal power in the viewing zone 32 and the portion 40represents the constant dioptric focal power in the viewing zone 34, theconstant dioptric focal power in the portion 40 being of a greatermagnitude than that in the portion 32. The sloping portion 42 of thepower law defines that the dioptric focal power through the intermediatearea 36 changes at a constant rate. This is a typical type of power lawoften utilized in progressive power ophthalmic lenses. Of course, theheight h is variable and may be increased to the full height of thelens.

The power law shown in FIG. 3 is linear through the progressive powerviewing zone. The power law need not be linear and may be of anyarbitrary character as required by a particular application. It should,however, be a continuous curve through the progressive power viewingzone although it is not intended that minor discontinuities should beexcluded from the scope of the invention.

The basic construction of the progressive power surface of FIG. 3 isshown in FIG. 4. This construction, however, does not incorporate per sethe novel features of the present invention which will be describedherebelow. The progressive power refractive surface is generated by acircular arc C of variable radius and constant inclination which passessuccessively through all points Q of the principal meridional line. Theaxis aa' of the generating circle lies in the principal meridionalplane, and makes a constant angle with the vertical. The radius vectorQq defines point q on the evolute for a given point Q of the principalmeridional line. The radius QR of the generating circle passing througha given point Q is determined by the condition that its axis aa' passthrough the corresponding point q of the evolute 22. The radius of thegenerating circle equals the length of the line segment QR of FIG. 4.

It can be shown that, as a consequence of this construction, theprincipal curvatures at each point of the principal meridional line areequal. In other words, the surface is umbilic (free of astigmatism atthe principal meridional line).

It is convenient to describe the distortive properties of a refractivesurface such as those associated with the present invention in terms ofthe image of a square grid as seen through the lens. While not totallyaccurate, this test is a reasonable approximation of the visual affectgained by wearer of the resulting opthalmic lens.

Two general types of distortion can be distinguished, normal and skew.Normal distortion refers to the unequal image magnification in the twoorthogonal directions parallel to the lines of the grid. Skew distortionrefers to a departure from the orthogonality of the original grid lines.Suppose that a single square of such a grid is viewed through a smallarea of a given ophthalmic lens. If the principal axes of astigmatism inthat area of the lens are parallel to the lines of the grid beingviewed, then the image perceived shows pure normal distortion, i.e., theimage of the grid square is a rectangle whose sides are parallel tothose of the square. If the principal axes of astigmatism in that areaof the lens bisect the right angle between the respective orthogonalgrid lines, then the image shows pure skew distortion, i.e., the imageof the square is an equilateral parallelogram. In the general case,where the principal axes of astigmatism have arbitrary orientation withrespect to the lines of the object grid, the image of the squareperceived will exhibit a combination of normal and skew distortion,i.e., the image will be a non-equilateral parallelogram.

Of the foregoing two specific types of distortion, skew distortion is byfar the more objectionable in ophthalmic applications. In an ophthalmiclens, skew distortion produces a sensation of rocking and swaying withrespect to the environment. In most instances, this rocking and swayingeffect results in disorientation and nausea on the part of the wearer.The prior art progressive power and variable ophthalmic lenses wereeither totally uncorrected for skew distortion, resulted in only apartial correction for skew distortion, or resulted in a reading areatoo small for general use.

The astigmatism present in a refractive surface, for a linear power law,varies laterally at twice the rate of addition of focal power along theprincipal meridional curve. Therefore, unless correction or compensationfor distortion is undertaken in the peripheral areas of the ophthalmiclens utilizing progressive power, considerable distortion is necessarilypresent in the surface. For example, in the form of progressive lensshown in FIG. 3 of the drawing, the principal axes of astigmatism form a45° angle with respect to the horizontal and vertical lines of thevisual environment throughout the intermediate area 36. Therefore, theselenses give rise to substantial amounts of skew and normal distortion inthe peripheral areas of the intermediate area 36.

As has been stated above, as is the case with astigmatism in suchprogressive power refractive surfaces, it is not possible to eliminatedistortion in the surface. It has been discovered, however, that it isentirely possible to construct an ophthalmic surface which in theperipheral areas is totally corrected for skew distortion. That is tosay, the principal axes of astigmatism in the peripheral areas may becaused to lie in horizontal and vertical planes with respect to thevisual environment such that only normal distortion occurs in theseperipheral zones. This normal distortion is far less objectionable thanthe skew distortion and the incorporation of this aspect into aprogressive power lens forms one of the principal features of thepresent invention.

This corrected condition of the refractive surface in the peripheralareas for skew distortion can be most easily expressed mathematically byletting the lens surface be tangent to the X--Y plane at the origin ofthe coordinate system where the X-axis points downward in the directionof increasing optical power, and by assuming that the surface isrepresented by the following expression:

    Z = f(x,y)                                                 (1)

when y and x are the horizontal and vertical directions respectively andZ is the height of the surface from the xy plane, i.e., Z can berepresented by: ##EQU1## r_(D) = distance viewing zone meridionalradius, r = meridional radius of curvature, and v = various mathematicalexpressions dependent upon the portion or area of the lens surface beingdescribed.

The lens surface of the present invention is divided into viewing zonesand areas within some of those zones. In the upper half circle of thelens body, the far-vision or distance zone is provided. In accordancewith the mathematics of the specification, where r is the meridionalradius of curvature, in this zone r = r_(D) and v = y.

In the intermediate zone of height h (the progressively-varying opticalpower zone), r = (1/r_(D) + bx)⁻¹, where b = (1/h)(1/r_(R) - 1/r_(D)),and where r_(R) is the reading or near vision meridional radius. Thus,in the near vision zone, r = r_(R).

By way of further explanation, in the intermediate and near visionzones, there are three mathematical expressions for v, depending on thearea. In the area bisected by the vertical meridional line, v = y. Inthe outermost areas from the vertical meridional line, v is expressedas: ##EQU2## And in the two "blending" areas that lie between theoutermost areas and the central area, v is expressed as: ##EQU3## where:##EQU4##

If the surface has the condition that the directions of principalcurvatures, the principal axes of astigmatism, at all points lie inplanes which are parallel to the x and y axes, then

    δ.sup.2 f/δxδy = 0.                      (2)

When this expression is satisfied for all points in a given area, onlypure normal distortion may be perceived through the lens.

This partial derivative expression can be alternatively viewed as

    (δ/δx)(δ/δy) f(xy).

The two above partial derivative operators can be shown, by mathematicaltensor analysis which need not be repeated here to fully comprehend thepresent invention, to be substantially proportional to the cosines ofangles between surface grid lines, e.g., the grid lines of FIGS. 6-11.An angle for which the cosine is zero, as required by equation (2), is90°, the orthogonality angle. Thus, when partial derivative expression(2) is satisfied, orthogonality is provided and skew distortion isvirtually eliminated; vertical and horizontal lines in the visualenvironment appear to the wearer of the lens having this correction asvertical and horizontal respectively.

Yet another way of viewing the substantial significance of equations (1)and (2) is to appreciate first that in general cylindrical lens surfaceswith vertical and horizontal mutually orthogonal axes provide no skewdistortion, and second that for these orthogonally-oriented cylinderswith their axes co-linear with the Y and X coordinates axesrespectively, equation (1) can be separated into:

    Z = f(xy) = f.sub.1 (x) + f.sub.2 (y)                      (8)

where f₁ (x) is a function only of the x variable and f₂ (y) is adifferent function only of the y variable. By operating on equation (8)with the operators of equation (7) one necessarily obtains zero, since:##EQU5## Thus, the zero condition of equation (2) implies thiscylindrical axial orthogonality condition which provides zero skewdistortion.

Referring now to FIG. 5 of the drawing, there is shown a progressivepower ophthalmic lens 50 according to the present invention. A principalmeridional line 52 bisects the lens in a generally vertical direction.Once again, the lens 50 is divided into three juxtaposed viewing zones54, 58, and 56 respectively one above the other. The uppermost viewingzone 54 is formed with a refractive surface having a constant dioptricfocal power to accommodate for distant vision. The lower viewing zone56, in the central regions thereof, is formed with a second, higherconstant dioptric focal power surface adapted for near vision. Theintermediate zone 58 which is disposed between the near and far viewingzones 54 and 56, respectively, provides progressive transitionaldioptric focal power therebetween. As described thus far, the lens ofthe invention is not appreciably different from those of the prior art.The technique for generating the lens in the portions adjacent to theprincipal meridional curve is that described with reference to FIG. 4.The meridional power law is of any generally acceptable form such asthat shown in FIG. 3.

In the intermediate and near vision zones 58 and 56, the refractivesurface of the progressive power lens 50 is further subdivided laterallyinto five areas. The dividing lines between these areas AB, CD, A'B',and C'D', are chosen arbitarily with respect to shape and position.Although illustrated as being symmetrical with respect to the principalmeridional curve 52, this is not a condition of the invention. In thepresent embodiment, the dividing lines A'F'B' and C'D' may be mirrorimages of AFB and CD with respect to the principal meridional line 52.The central area A'AFF' is formed in accordance with any chosenprogressive power ophthalmic lens design.

The peripheral areas of the refractive surface CDE and C'D'E' areconstructed to connect smoothly to the far vision viewing zone 54 alongthe lines CE and C'E'. The smooth optical connection is achieved byhaving a smooth unbroken surface over the entire lens. At each point inareas CDE and C'D'E', the principal axes of astigmatism lie inhorizontal and vertical planes according to the foregoing expression. Itfollows that, when viewed through these peripheral areas of theprogressive power ophthalmic lens, the horizontal and vertical lineswithin the visual environment are not subjected to skew distortion.Furthermore, when viewed through the periphery of the lens a verticalline will remain vertical and unbroken throughout the total height ofthe periphery of the lens. In other words, a line which is viewed asvertical in the peripheral portions of the far vision viewing zone 54continues vertical and unbroken in the intermediate viewing zone 58 andthe near vision viewing zone 56.

The intermediate regions ABDC and A'B'C'D' are areas of optical blendingbetween the central portion and the skew distortion corrected peripheralportions of the ophthalmic lens 50. The purpose of these areas is toprovide a smooth optical connection between these areas of diverseoptical functions. Once again, these areas also connect smoothly to thefar vision area 54. The precise choise of refractive surfaceconfiguration within these areas of blend depends on a great number offactors. These include the amount of add present in the lens, theoverall width of the lens, and the height of the intermediateprogressive power viewing zone 58.

As noted earlier, the principal axes of astigmatism lie in planes at 45°to the vertical in the center progressive power area when the power lawis linear therein. Also the principal axes of astigmatism in theperipheral areas CDE and C'D'E' are in vertical and horizontal planes.In other words, the distortion in the center is pure skew distortion andin the periphery, pure normal distortion. The areas of blending ABDC andA'B'D'C' have aspherical surfaces which serve to transform theorientation of the principal axes of astigmatism between the other areassmoothly so that discontinuities are not introduced into the surface orimage. The width of the areas of blend is, however, variable and may asa limiting case be reduced to zero. In other words, the purview of theinvention extends to those cases where there are only the central andperipheral areas present in the refractive surface.

It is also within the purview of the invention that the peripheral areasCDE and C'D'E' may actually fall outside the area of the lens, in whichcase the blending areas ABDC and A'B'D'C' become, in effect, theperipheries of the lens. The areas CDE and C'D'E' serve the purpose ofproviding a basis for defining the form of the areas ABDC and A'B'D'C'.A lens having this form does not completely correct for skew distortionin the peripheral areas of the lens. The effect of skew distortion is,however, softened in comparison with that found in the lens of FIG. 3.The advantage of such a lens is that it can be made to have onlymonotonically changing curvatures. This means that, although skewdistortion is not entirely corrected, the lens nevertheless shows asmooth lateral optical effect.

With respect to the following examples, the basic differences betweenthe surfaces are illustrated in the drawing by the differences in thedistortion present in the image of a square grid. In each of thefollowing cases, only one-half of the image is presented, the other halfbeing essentially identical therewith.

Referring initially to FIG. 6 of the drawing, the peripheral areas ofthe intermediate and near vision viewing zones have aspherical curvatureof the same radius and center as the constant dioptric focal power farvision viewing zone. This is a limiting case where the criteriapreviously set forth for the peripheral areas is satisfied by acontinuation of the upper spherical surface into the lower reaches ofthe progressive power ophthalmic lens. There is, therefore, nodistortion or astigmatism attributable to progressive power which existsin these peripheral areas of the lens. On the other hand, the blendingareas intermediate between the central progressive power area and theperipheral areas contain large amounts of distortion when the grid isviewed through them.

The refractive surface depicted by the image of FIG. 7 is formed so thatthe variation in vertical magnification in the peripheral areas of thelens is identical to the variation of vertical magnification along theprincipal meridional line. Therefore, the distortion of a horizontalline of the grid as seen through the lens is such that the level of theline at the periphery is identical to its level at the principalmeridional line. The astigmatism which is present at any level of theperiphery is equal to the rate of add at the principal meridional lineat the same level. The distortion produced by the blending between thecentral area of the lens and the peripheral areas is considerably lessthan is produced in the limiting case lens of FIG. 6.

FIG. 8 shows the image of a limiting example according to the presentinvention. Here, the width of the blending regions is reduced toessentially zero. Thus the downward curving lines of the intermediateprogressive power area turn abruptly horizontal at the periphery of thecentral area. This design minimizes the area of the lens over which theobjectionable skew distortion occurs. This design may have an additionaladvantage in that the width of the spherical near vision area, shown bythe enlarged square portion of the grid, is increased over that of theprevious examples.

Referring now to the grid image shown in FIG. 9 of the drawing, here thelens refractive surface is designed to provide that the horizontal linesof the grid are bell-shaped as seen through the intermediate progressivepower viewing zone of the lens. The laterally disposed blending areasare necessarily of substantial width and the surface within these areasis designed specifically to provide the smoothest optical effect as theline of sight moves from the center of the lens toward the periphery.

The lens which provides the image shown in FIG. 10 is very similar tothat utilized for FIG. 9 except that the periphery of the near visionarea has been altered slightly in order to relieve the bunching of thehorizontal lines that appear near the lower boundary of the intermediatearea of the lens of FIG. 9. Obviously, in the lens utilized for FIG. 10,a controlled amount of skew distortion is introduced deliberately intothe lower peripheral areas of the near vision viewing zone in order torelieve the bunching effect. While this initially appears somewhatobjectionable as shown by the grid image of FIG. 10, it must beremembered that a typical ophthalmic lens is cut with an edgeconfiguration to fit standard spectacle frames and that the majority ofthe corner portions of the grid of FIG. 10 will not be present in thecompleted ophthalmic lens. Therefore, this controlled amount of skewdistortion is not considered to be objectionable.

In each of the examples shown in FIGS. 6 through 10, it has been assumedthat the blending areas ABCD and A'B'C'D' have vertical boundaries. Itshould be emphasized that as is shown in FIG. 5, the boundaries inquestion need not be vertical, and, in fact, there are specificadvantages attributable to non-vertical orientation of the boundaries ofthe blending areas. An example of an image of a lens having suchconfiguration is shown in FIG. 11. Here the boundaries are non-verticalas shown by the superimposed dotted lines spread out near the bottom ofthe lens. This provides a design that has the advantage that thedistortion is kept to a minimum in the upper half of the intermediateviewing zone and at the same time provide a conveniently wide constantdioptric focal power near vision viewing area.

Therefore, it can be seen that in the foregoing examples acuity in theperipheral areas of the near vision viewing zone of the progressivepower ophthalmic lens is sacrificed from that in the prior art designsin order to correct for skew distortion in the peripheral areas of theintermediate viewing zone of the lens. This is accomplished whilesucceeding in maintaining the constant dioptric focal power near visionarea of the lens at acceptable proportions.

Thus far, the foregoing discussion has considered only those lenses thatare symmetrical about a principal vertical meridional line, i.e., theprincipal vertical meridional line is in fact vertical on the surface ofthe ophthalmic lens and precisely divides the lens in symmetricallateral portions. From the point of view of product inventory, suchperfectly symmetrical lenses are extremely advantageous. With propermarking applied, a symmetrical lens blank can then be used for either aleft or right eye lens. Functionally, however, it is preferable todesign the progressive power ophthalmic lenses separately for the leftand right eyes respectively. The resulting lenses are asymmetrical sincethe interpupilary spacing of human beings decreases as their focuschanges from distant objects to nearby objects. Therefore, in fittingthe symmetrical lens to the patient, the principal meridional line ofsymmetry should be inclined approximately 10° from the vertical toprovide an effective inset of the near vision viewing zone. This 10°rotation of the lens about its central point ensures that the line ofsight can pass along the principal vertical meridional line for clearvision at all distances.

However, once the lens has been rotated accordingly, the principal axesof astigmatism in the periphery of the symmetrical skew distortioncorrected lens described hereinabove are no longer aligned with thehorizontal and vertical elements of the visual environment. Therefore,particularly in the case of those lenses with higher adds, thismisalignment may result in noticeable incorporation of skew distortionthroughout the peripheral areas of the opthalmic lens. This, of course,would be objectionable for the identical reasons that those lenses ofthe prior art were objectionable to many wearers. Such a lensis shown inFIG. 12, where the orientation of a principal axis of astigmatism isshown at points in the various areas when the lens is rotated 10°.

It is, therefore, included within the purview of the present inventionto correct this situation by modification of the foregoing symmetricaldesign. In the modified versions, the far vision viewing zone and thecentral portions of the intermediate and near vision areas remainunchanged from the foregoing symmetrical design. However, the peripheralareas of the intermediate and near vision viewing zones are modifiedsuch that when the principal meridional line is inclined approximatelyat 10° with respect to the vertical, the principal axes of astigmatismin these peripheral zones again are aligned with the horizontal andvertical elements in the visual environment. The blending areas areappropriately modified as well in order to provide a smooth opticalcorrection between the central portions and the peripheral areas. FIG.13 illustrates the orientation of the principal axes of the astigmatismat various locations for both a right and a left lens modified tocompensate for the decreasing interpupilary spacing at near vision.

As was explained hereinabove, the prior art agrees quite generally onthe conditions which exists along the principal vertical meridionalline. The prior art consists largely of a series of attempts to acquirea means for generating the resulting aspherical surface. This generationproblem caused certain limitations to exist in the design of the lens.The present lens has avoided this situation by discarding therequirement for ascertaining a precise means of generating directly afinished ophthalmic lens. The lenses according to the present inventionmay be formed directly or as cast lenses. The lenses are formed byprogramming initially a machine such as a numerically controlled millingmachine to produce essentially the complement of the refractive surfacein a porous ceramic block. After the complementary surface is formed, avacuum is applied to the back surface of the ceramic block and a sheetof highly polished glass is heated and slumped into the cavity formed inthe ceramic block. This glass sheet may then be polished to formdirectly the refractive surface on a blank. Alternatively, the oppositeside of the glass plate from that which comes into contact with theceramic block may be used to form a mold surface for casting plasticlenses according to the present invention.

This casting technique has numerous advantages, not the least of whichis that a lens comparable in price to present glass ophthalmic lensesmay be produced. However, additional advantages inhere in the processdue to the fact that the glass sheet slumped into the ceramic block hasfinite thickness. The finite thickness tends to blend any localdiscontinuities which may exist in the surface such as are producedbetween adjacent cuts of the grinding tool in the generating machine.The resulting lens has a smooth optical quality refractive surfacethereon.

It can be shown that, when the power law within the intermediateprogressive power viewing zone is linear, i.e., a constant rate ofaddition, as is the case for the power law of the progressive power lensshown in FIG. 3 of the drawing, the astigmatism increases withperpendicular distance from the principal vertical meridional line attwice the rate of add of dioptric power along the principal verticalmeridional curve. Thus, if the add is B and the intermediate area is ofheight h, then the astigmatism A at a distance y from the meridionalline is given by

    A = 2 B/h y

The "corridor of clear vision" is defined as that region of theintermediate viewing zone bounded on the right and left sides by lineshaving one diopter of astigmatism. (It is known that 1.0 diopters ofastigmatism reduces visual acuity by approximately one-half). Forexample, if B equals 2.0D and h equals 10mm, then from the foregoingequation, the width w of the corridor of clear vision is 5.0mm. Fromthis typical example, it is clear that a considerable price is paid forthe feature of progressive power in the intermediate viewing zone. Thatis, the visual acuity in the intermediate viewing zone is very pooreverywhere except through a narrow central corridor, the width of whichis controlled largely by the height of the intermediate viewing zone andthe rate of add.

The difficulty of having a narrow central corridor of clear vision canbe at least partially relieved by combining the progressive powervariation with finite power discontinuities at either or both of theboundaries separating the intermediate viewing zone from the far visionand near vision viewing zones. The solid curves shown in FIGS. 14A, 14Band 14C represent alternative progressive power laws incorporating suchdiscontinuities. FIG. 14A shows the meridional power law of aprogressive power ophthalmic lens according to the invention which has apower discontinuity, i.e., a jump, at the upper boundary of theintermediate viewing zone, but no such discontinuity at the lowerboundary. In FIG. 14B, the situation is reversed with the powerdiscontinuity occurring only at the lower boundary of the intermediateviewing zone. FIG. 14C shows the meridional progression of power in alens having finite discontinuities at both the upper and lowerboundaries of the intermediate viewing zone. In each of these examples,the dotted line superimposed on the power law diagram corresponds to thepower law of a progressive power lens having no power discontinuities atthe boundaries of the intermediate viewing zone.

A simple inspection of FIGS. 14A-14C provides a clear indication thatthe power law discontinuities have the precise effect of reducing therate of addition of dioptric focal power across the intermediate viewingzone. Therefore, by the foregoing relationship, the corridor of clearvision is thus appreciably widened. If the power discontinuities havemagnitudes b₁ and b₂, then, from the foregoing equation, the astigmatisminside the intermediate area will be given by ##EQU6##

Suppose that B once again equals 2.0D, h equals 10mm, and b₁ and b₂equal 0.5D each. Now the width w of the corridor of vision becomes 10mm.This is a 100 percent improvement in width over the case of a continuouspower law previously described, i.e., where b₁ =b₂ =0. The table of FIG.15 gives the width of a corridor of clear vision for various totaladditions B and total discontinuous power variations (b₁ +b₂) as the topnumber in each block. The lower number is the percentage increase of wover the width associated with a continuous power law.

The magnitude of an individual power discontinuity should not be sogreat as to destroy the wearer's sense of visual continuity intended bythe concept of progressive power. This criteria would probably limitsuch individual discontinuities to about 0.5 diopters. However, it isintended that discontinuities greater than 0.5 diopters be includedwithin the purview of the present invention.

The use of power discontinuities also helps to reduce the distortionthrough the intermediate viewing zone. FIG. 16 shows the distortion of asquare grid as viewed through a progressive power ophthalmic lens havinga continuous power law. This image is similar to the grid which would beobserved through a progressive power lens such as shown in FIG. 3. Onthe other hand, FIG. 17 shows the distortion of the same grid whenviewed through a progressive power lens having finite powerdiscontinuities at both the upper and lower boundaries of theintermediate progressive power zone. In both cases the power law withinthe intermediate viewing zone is linearly increasing and the total addis equal. Obviously, the distortion of the grid within the intermediateviewing zone in the lens shown in FIG. 17 is markedly less than that ofthe lens shown in FIG. 16.

If a progressive power lens as defined in the prior art were to haveincorporated therein finite power discontinuities, the price paid forsuch discontinuities would be the appearance of a ledge, i.e., adistinct break in the surface continuity extending across the surface ofthe lens at the level of the power discontinuity. If, for example, theaxis of the generating circle as defined in FIG. 4 is vertical, theledge associated with a power discontinuity would make a horizontal lineacross the lens. The height L of this ledge grows approximatelyquadratically with distance y from the meridional line according to thefollowing relationship

    L = 1/2 b/n-1 y.sup.2

For example, if b equals 0.5D and n equals 1.5, then at y equal to 35mm,L equals 0.62mm. If the cosmetic advantages of progressive power lensesare to be maintained, this ledge would then have to be blended into theviewing zones which it separates. This would be extremely difficult inthe prior art progressive power lenses. However, with the process ofsagging mold surfaces utilized in the present invention, the blendingoccurs automatically by virtue of the finite thickness of the sheet ofglass utilized to form the mold surface. The resulting lens thencontains blended areas 60 of rapidly changing power as indicated in FIG.18. These areas are not likely to be troublesome visually since they areadjacent to those portions of the intermediate viewing zone where thevisual acuity is already severely diminished by surface astigmatism.

As previously stated, two types of advantages inhere to lenses of thegeneral class including the present invention. These are continuousaccomodations throughout the height of the lens, an optical advantage,and invisible dividing lines between the various viewing zones of thelens, a cosmetic advantage. It has been shown that a price is paid forthe advantage of progressive accomodation along the principal verticalmeridional curve, that is, in the intermediate viewing zone visualacuity is diminished severely except along a relatively narrow corridorof clear vision centered on the principal meridional line. If, however,the wearer is willing to sacrifice the advantage of progressiveaccomodation, it becomes possible utilizing power discontinuities tosubstantially widen the corrider of clear vision and still retain thecosmetic advantage which adheres to progressive power ophthalmic lenses.

For example, in an ordinary solid type trifocal lens which is commonlycommercially available today, the dividing lines between the far,intermediate, and near vision segments are highly visible. This iscaused by the presence of ledges at the dividing lines which growquadratically in height with the distance from the center principalmeridional line. The ledge height is confined to zero at the principalmeridional line but the ledge height at a distance of 35mm from theprincipal meridional line where the change in focal power betweenadjacent segments is 1.0D, is 1.24mm. A ledge of this height is highlyvisible and no method of manufacture including the sagging block methoddescribed hereinabove can effectively hide such a ledge.

It is, however, within the purview of the present invention to form amultifocal lens wherein the theoretical ledge height is restricted tosome minimum value which can be effectively blended out through thesagging process of manufacture.

Such a multifocal lens is shown in FIG. 19 of the drawing. Themeridional power law has the stepwise form of the ordinary trifocal andis shown at the right of FIG. 19. If b₁ and b₂ are the values of thepower discontinuity steps and B is the total add, then

    B = b.sub.1 +b.sub.2.

In the case where either b₁ or b₂ equals zero, the lens simply becomes abifocal ophthalmic lens. The multifocal lens 100 shown in FIG. 19 isformed of a constant dioptric focal power distance viewing zone 104, asecond viewing zone 106 disposed directly below the distance viewingzone 104, and a third viewing zone 108 at the bottom for viewing nearbyobjects. Once again, the intermediate and nearer viewing portions aredivided laterally into at least three, and preferably five areas. Thecentral area ABB'A' is centered on the principal vertical meridionalline 102 and is comprised of two constant dioptric focal power areasobeying the power law shown at the right of FIG. 19. Adjacent to thecentral zone are blend areas ACDB and A'C'D'B'. These areas of blendperform the same function as those areas of blend shown in FIG. 5 forthe progressive power lens. Similarly, peripheral zones CDE and C'D'E'also are again corrected for skew distortion in the manner describedhereinabove. In these peripheral areas of the intermediate and nearvision zones, a vertical line of the environment is viewed through thelens as an unbroken vertical line from the top to the bottom of thelens. In other words, along any vertical line drawn through theperiphery of the lens, the amount of horizontal prism is constant.

The condition of verticality of lines used for the periphery of the lensis equivalent to the correction of skew distortion, which in the case ofordinary solid type trifocals is concentrated at the horizontal ledgesthat are associated with the various power steps.

The principle advantage arising from the correction of skew distortionis the reduction of the height of the horizontal ledges. The ledges arenot removed entirely but the height that remains can be renderedcosmetically invisible by use of the sagging method of manufacture. Forexample, consider the type of distortion correction in which the widthof the blending areas ABDC and A'B'D'C' are reduced to zero, i.e., theblending is done abruptly. The distortion of a squared grid as seenthrough such a multifocal lens is illustrated in FIG. 20 of the drawing.Suppose that the width of the central region A' AB B' is taken as 24mm.If the change in dioptric focal power at the boundaries of theintermediate zone is taken as 1.00D, then, the ledge height L where yequals 12mm, is 0.14mm. The ledge height L where y is greater than 12mmremains constant and equal to 0.14mm. Although on a generated lens, aledge of this height would still be easily visible, the height L is notso great that it cannot be smoothed out and made cosmetically invisiblein the foregoing sagging method of manufacture. The area of blendproduced by this process is indicated at 110 in FIG. 21 of the drawing.

The type of multifocal lens thus produced compares favorably to thesegment type multifocal currently available. However, the dividing linesbetween the various portions of the lens are not visible in the lensaccording to the present invention as they are in the segment typemultifocal lens.

Throughout the foregoing discussion of the various features of theinvention, the various features of the lenses according to the inventionhave been discussed independently. That is, the vertical discontinuitiesconcept has been discussed separately from the feature of dividing thelens horizontally into areas which are treated separately in order tocorrect for skew distortion. It is, however, included within the purviewof the invention to combine these various features in variouscombinations in order to provide optimal performance of a progressivepower ophthalmic lens for particular ophthalmic requirements.

A detailed description of the design and manufacture of a progressivepower lens of the type depicted in FIG. 11 will now be given. The lensis to be made of plastic, cast in a mold made by the slumping processdescribed above.

Therefore, in the manner of design, what is needed is a detaileddescription of the surface of the ceramic block on which the glass moldis to be slumped. The curvatures of the block must be such that theresultant mold produces the lens depicted in FIG. 11. The rectangularcorrdinate system used is shown in FIG. 23. This view shows the concavesurface of the block. The surface is tangent to the xy plane at theorigin 0. That portion of the block corresponding to the distanceportion of the mold and lens lies above the xy plane. Those portionsthat correspond to the intermediate and reading areas lie below thatplane. The intermediate area is of height h. The block is symmetricalabout the xz or meridional plane. On the lower halfof the block, thelateral blending zone on the right-hand side is bounded on the left andright by the curves y = y₁ (x) and y = y₂ (x), and the lateral blendingzone on the left hand side is bounded on the right and left by thecurves y = y₁ (x) and y = y₂ (x). The radius of curvature of thespherical distance portion of the block is r_(D), that of the sphericalreading portion r_(R). In general, the radius of curvature at a point xon the vertical meridian is given by r = r(x). The form of the surfaceof the block, expressed as an elevation z = f(x,y) above the xy plane,is given by the set of equations presented earlier, viz. Equation (3)and subsequent related expressions.

Restating these equations employing terms previously utilized andemploying certain terms which further simplify the mathematics, weobtain: ##EQU7## where the functions Q, r and u have their previousmeanings, and K = 0 in the central portion of the slumping block, K = Y²-n in the peripheral portions of the slumping block, K = 1(y-y₁)³-m(y-y₁)⁴ in the blend zones of the block where l, m, and n areidentical to that which was given earlier.

As noted in the foregoing paragraph these equations define the surfaceof the ceramic block against which the mold is slumped employing aprocess previously described and to be further detailed. The glassemployed is an ophthalmic crown glass, which is placed on this ceramicblock defined by the equations presented and the combination is insertedinto an oven which is heated as follows. The temperature is raised inthe oven to a maximum temperature of approximately 1210° F. over aperiod of time of approximately 4 hours. The temperature in the oven iscontained at this value for approximately 1 hour. Then, approximately 8hours are utilized to reduce the temperature in the oven from this valuedownward.

By way of example, with regard to FIG. 24 let it be required tomanufacture a CR-39 plastic ophthalmic lens having a distance portionwith convex radius of curvature 83.33 mm and having a reading additionof 2.00 diopters. The mold will be slumped starting with a meniscusglass blank having surface powers of +6.00 and -6.37 diopters and havinga center thickness of 4.0 mm. It has been determined that in order toobtain a lens with the stated refractive characteristics and using aglass slumping blank of the above description, the radii of curvature ofthe spherical portions of the block have to be 88.113 mm, and 68.440 mm,for the spherical distance area and for the spherical reading arearespectively. Assuming that the rate of add at the principal meridionalline inside the intermediate area is linear, the curvature law for theintermediate area may be written:

    1/r = 1/r.sub.D + (1/r.sub.R - 1/r.sub.D)x/h

If h = 10.0 mm, this law becomes for the above radii

    1/r = (11.3491 + 0.3262 x) 10.sup.-3 , mm.sup.-1.

The lines y₁ and y₂ are chosen to be straight lines with the followingcoordinates

    ______________________________________                                        x (mm)       Y.sub.1 (mm)                                                                             Y.sub.2 (mm)                                           0           7.0        14.0                                                  10           9.1        18.2                                                  ______________________________________                                         The equations of these lines are thus

    Y.sub.1 = 7.00 + 0.21 x                                    (mm)

    Y.sub.2 = 14.0 + 0.42 x                                    (mm)

These values of r_(D), r_(R), r, Y₁, and Y₂ may now be substituted intothe equations of the surface. A computer was programmed in accordancewith the above equations and input data to guide a cutting tool whichgenerates the required surface onto the ceramic slumping block. FIG. 24shows the results of the electronic computer evaluation employing theabove input data which gives the elevation of the surface of theslumping block at 4 mm intervals over the area of a block 86 mm indiameter. Only one-half of the block is depicted. The other half of theblock is not depicted since it is an essential mirror image of the halfpresented. Each number represents the z-direction distance from thesurface of the block, at the center of the cell in which the numberappears, to the xy plane that is tangent to the surface of the block atthe center of the cell designated 0.0000. The vertical meridian 52 ofFIG. 5 would therefore intersect the center of the cell designated0.0000 as well as the centers of the cells directly above and below thiscentral grid, i.e.: the centers of cells bearing measurements: 0.0908,0.3639, 0.0943, 0.3919, etc. This particular exemplary embodimentapplies to a ceramic slumping block having distance and near-zero radiiof 88.113 and 68.440mm which is used to slump a mold for casting aplastic lens of the form depicted in FIG. 11 having a distance radius of83.33 mm and a reading addition of 2.00 diopters.

Although the foregoing mathematical and textual description issufficiently precise and accurate for one to construct a progressivepower lens in accordance with the principles of my invention, andalthough the exemplary embodiment as shown in FIG. 24 is derived from acomputer analysis of the equations presented thus far, there is anothermathematical formulation based on surfaces of revolution which can beemployed to help conceptualize of understand the principles involved.However, since these other mathematical formulations may not lendthemselves readily to computer analysis, they are presented merely as atool of insight and to provide another point of view.

To begin with, to correct for skew distortion in peripheral areas of theprogressive power zone, one requires that vertical and horizontal linesin the environment are preceived by the wearer of a skew-distortioncorrected lens as being respectively vertical and horizontal. Thiscorrection can be achieved by requiring that these peripheral areascomprise portions of a surface of revolution. The axis of the surface ofrevolution is vertical, and lies in the vertical meridional plane. Bysymmetry it should be clear that the principal axes of astigmatism atevery point of such a surface of revolution lie in horizontal andvertical planes. Therefore, when the peripheral areas of the lens havethis form, only pure normal distortion may be perceived through thoseareas.

Referring to FIG. 5 and FIG. 22, the peripheral areas of the refractivesurfaced CDE and C'D'E' are portions of a surface of revolution whoseaxis LL' is vertical and lies in the vertical meridional plane. For thesituation where the entire distance portion, comprising the upper halfof the lens, is spherical, the axis of revolution for peripheral regionsCDE and C'D'E' passes through the center of curvature of the distanceviewing zone. If the axis were to pass through any other point of theevolute 22, it would not be possible to smoothly connect the lower halfof the lens with the spherical upper half. In other words, because theequatorial dividing line EE' is circular, the axis of revolution for theperipheries of the lower half of the lens must pass through the centerof that circle.

Further in connection with FIG. 22, in designing such a lens thelocations of the lateral dividing lines AB, CD, A'B', and C'D' are firstdecided upon. Then with the knowledge that peripheral areas are to beportions of a figure or surface of revolution, the lateral blendingzones are designed in such a way that the smoothest possible connectionis achieved between the central and peripheral portions of the lens. Theperipheral regions are then formed by rotating the boundary curves CDand C'D' about the rotation axis LL' of FIG. 22. The general setequations applicable to a lens of the type depicted in FIG. 11, or to aslumping block that may be used to make such a lens, will now be given.These equations express the elevation z = f(x,y) of the surface abovethe xy plane. They give explicitly the form of the rotationallysymmetric peripheral zones.

For the spherical distance zone,

    z = r.sub.D - (r.sub.D.sup.2 -x.sup.2 -y.sup.2)1/2.

For the central portion of the lower half of the lens or block,including both the intermediate and reading levels ##EQU8## where u =Qr, and ##EQU9##

For the rotationally symmetric peripheral areas of the lower half of thelens or block, ##EQU10##

For the blending areas between the central and peripheral areas,##EQU11##

These equations, while providing an exact description of the geometricalproperties required of the lens or block, and which are mathematicallydescriptive of the portions of the surface of revolution earlierreferred to, are nevertheless quite complicated and are resistant toready numerical evaluation. Therefore, the former simpler set ofmathematical equations were used to generate the exemplary embodiment ofthe present invention as depicted in FIG. 24 herein.

Referring back to FIG. 17 in particular, it will be noted that, althoughthe introduction of discontinuities in the meridional power law hasreduced the level of aberrations in the intermediate area as comparedwith the aberrations of FIG. 16, there is still present a certain amountof skew distortion in the intermediate area. The skew distortion in theperipheries of the intermediate area can be turned into the lessundesirable normal distortion in exactly the same way as it wasaccomplished for the progressive power lens with continuous meridionalpower law. The intermediate and reading levels of the surface of thelens of FIG. 17 are divided laterally into 5 contiguous areas just asshown in FIG. 5. The central region remains as shown in thecorresponding area of FIG. 17. The peripheral areas, however, are nowformed in accord with the construction of FIG. 5, i.e., these areascomprise portions of a surface of revolution whose axis is vertical andpasses through the center of curvature of the distance portion. Becauseof this construction, the principal axes of astigmatism in theperipheral zones lie in horizontal and vertical planes, thus ensuringthat horizontal and vertical lines of the visual field will be perceivedthrough those areas as being horizontal and vertical. The areas betweenthe central and peripheral areas serve to blend the latter areassmoothly into each other. FIG. 25, which may be compared with FIG. 17,illustrates this correction of skew distortion in the peripheries of thelens, and also the smoothing provided by the slumping process of thesurface discontinuities at the upper and lower boundaries of theintermediate area.

An example of the design and manufacture of a lens of the type depictedin FIG. 25 will now be given. As in the case of the progressive powerlens illustrated above, the lens illustrated here is to be made ofplastic, cast in a mold made by the slumping method. Therefore, adetailed description of the curvature of the ceramic slumping block isrequired. The geometrical layout of the various viewing and blendingzones is identical to that shown in FIG. 23. Furthermore, the generalequations for the lens with continuous power law are also applicable tothe lens with discontinuous power law, except that the meridionalcurvature law must be replaced by ##EQU12## where r_(D) = radius ofcurvature of spherical distance zone

r_(R) = radius of curvature of spherical reading zone

δK₁ = curvature jump at DI-IP boundary

δK₂ = curvature jump at IP-RP boundary

h = height of intermediate area,

and it has been assumed that the meridional law of curvature is linearwithin the intermediate zone.

It is required to manufacture a CR-39 lens with distance portion withconvex radius of curvature 83.33 mm and with reading addition 2.00diopters. Power jumps of 0.5 diopters will be introduced at the upperand lower boundaries of the intermediate area. Using the same glassslumping blank as was used for the example of the continuous progressivepower lens, the following values of the input parameters are required toproduce a CR-39 lens with the stated optical characteristics:

r_(D) = 88.113 mm

r_(R) = 68.440 mm

δK₁ = (0.815) 10⁻³ mm ⁻¹

δK₂ = (0.815) 10⁻³ mm⁻¹

h = 10 mm

Thus, the meridional curvature law becomes ##EQU13## and as before Y₁ =7.00 + 0.21 × (mm)

H₂ = 14.0 + 0.42 × (mm)

These values of r_(D), r_(R), r, y₁ and Y₂ are now provided to acomputer which has been programmed to compute the surface elevation ofthe ceramic block at 4 mm intervals over the area of a block 0.86 indiameter. The computations are performed using the simplified set ofequations defined previously. FIG. 26 shows the results of thecomputation.

While there have been shown and described what are considered to bereferred embodiments of the present invention, it will be obvious tothose skilled in the art that various changes and modifications may bemade therein without departing from the invention as defined in theappended claims.

I claim:
 1. An ophthalmic lens comprising a lens body having a firstrefractive surface viewing zone thereon characterized bya smooth,unbroken principal meridional curve having continuously varying slopelying along the refractive surface viewing zone in a generally verticaldirection and dividing the refractive surface viewing zone into twosimilar lateral portions, the curvature of the principal meridionalcurve varying progressively from point to point therealong to provide apredetermined dioptric focal power at each such point according to apredetermined law, the dioptric focal power increasing generally fromtop to bottom of the viewing zone along the principal meridional curve,and being characterized further by having cross curves defined on therefractive surface viewing zone by planes perpendicular to the principalmeridional curve, the curvatures of the cross curves at their points ofintersection with the principal meridional curve being respectivelyequal to the curvature of the meridional curve at the point ofintersection, the first refractive surface viewing zone defined by apower range varying from a first dioptric focal power at the top of theviewing zone to a second, higher dioptric focal power at the bottom ofthe viewing zone, the viewing zone being divided into at least threelaterally disposed areas, a first one of the three areas being centrallydisposed in the viewing zone, extending vertically therethrough, andhaving the principal meridional curve passing through the centerthereof, the two outermost of the three areas being disposed at thelateral peripheries of the viewing zone and each having a surface whichcomprises a portion of a surface of revolution whose axis of revolutionis vertical and lies in the meridional plane whereby said lateralperiphery surface is so curved that the condition δ² f/δx δy = 0 isfulfilled when x and y are the coordinates in the vertical andhorizontal directions respectively of said outermost areas andf is thedistance of the refractive surfaces from the x-y plane whereby skewdistortion is so optically compensated that at all points on saidoutermost areas the principal axes of astigmatism lie in vertical andhorizontal planes which are parallel to the x and y axes respectively topermit a wearer of the lens to perceive horizontal and vertical lines inthe visual environment as being horizontal and vertical; and a secondviewing zone in vertical juxtaposition to the first viewing zone, thesecond one of the viewing zones having a constant dioptric focal powertherethrough, there being a downwardly positive discontinuity indioptric focal power of less than about 0.5 diopters at the boundarybetween the two viewing zones.
 2. An ophthalmic lens according to claim1, in which a third viewing zone is defined on the refractive surface inother vertical juxtaposition to the first one of the refractive surfaceviewing zones, the third viewing zone having a constant dioptric focalpower therethrough, the constant dioptric focal power in the thirdviewing zone being equal to the dioptric focal power at the otherjuxtaposed end of the range of dioptric focal power in the first viewingzone.
 3. An ophthalmic lens according to claim 1, in which a thirdviewing zone is defined on the refractive surface in other verticaljuxtaposition to the first one of the refractive surface viewing zones,the third viewing zone having a constant dioptric focal powertherethrough, there being a second downwardly positive discontinuity indioptric focal power of less than about 0.5 diopters at the boundarybetween the first and third viewing zones.
 4. A progressive powerophthalmic lens according to claim 3, in which the predetermined lawdefines a constant rate of change of dioptric focal power through thefirst viewing zone along the principal meridional curve.
 5. Anophthalmic lens comprising a single piece of lens material of apreselected index of refraction having a plurality of refractive surfaceviewing zones characterized by:a first viewing zone having asubstantially uniform predetermined dioptric focal power throughout anda surface so curved that the principal axes of astigmatism at all pointsthereon lie substantially in vertical and horizontal planes to permit auser of the lens to perceive horizontal and vertical lines in the visualenvironment as being respectively vertical and horizontal as viewedthrough said first zone; a second viewing zone of greater dioptric focalpower than that of said first viewing zone and a positive discontinuityof less than approximately 0.5 diopters of focal power between saidfirst and second viewing zones; the dioptric focal power of said secondviewing zone increasing progressively from point-to-point in a directionaway from said first viewing zone along a principal meridian dividingsaid second viewing zone into two similar lateral portions; the secondviewing zone having at least three viewing areas, a first of said areasbeing aligned and centered with said principal meridian intermediatelyof remaining laterally disposed areas each having a surface so curvedthat the condition δ² f/δxδy = 0 is fulfilled when x and y are thecoordinates in the vertical and horizontal directions respectively ofsaid outermost areas and f is the distance of the refractive surfacesfrom the x-y plane whereby skew distortion is so optically compensatedthat at all points on said laterally disposed areas the principal axesof astigmatism lie in vertical and horizontal planes which are parallelto the x and y axes respectively to permit the user of the lens toperceive horizontal and vertical lines in the visual environment asbeing horizontal and vertical when viewed through said remaininglaterally disposed areas, the surfaces of said laterally disposed areasfurther comprising a portion of a surface of revolution whose axis ofrevolution is disposed parallel to the direction of said principalmeridian of said second viewing zone; and all adjoining boundaries ofsaid first and second viewing zones and said viewing areas of saidsecond zone being smoothly surface blended.
 6. An ophthalmic lensaccording to claim 5 including a third viewing zone intermediately ofsaid first and second zones, said third zone having a substantiallyconstant dioptric power value no greater than that of any point on saidprincipal meridian of said second viewing zone and no less than that ofsaid first viewing zone, all adjoining boundaries of said first, secondand third viewing zones and said viewing areas of said second zone beingsmoothly surface blended.
 7. An ophthalmic lens comprising a lens bodyhaving a first refractive surface viewing zone thereon characterizedby:a smooth, unbroken principal meridional curve having continuouslyvarying slope lying along the refractive surface viewing zone in agenerally vertical direction and dividing the refractive surface viewingzone into two similar lateral portions, the curvature of the principalmeridional curve varying progressively from point to point therealong toprovide a predetermined dioptric focal power at each such pointaccording to a predetermined law, the dioptric focal power increasinggenerally from top to bottom of the viewing zone along the principalmeridional curve, and being characterized further by having cross curvesdefined in the refractive surface viewing zone by planes perpendicularto the principal meridional curve, the curvatures of the cross curves attheir points of intersection with the principal meridional curve beingrespectively equal to the curvature of the meridional curve at thepoints of intersection; the first refractive surface viewing zonedefined by a power range varying from a first dioptric focal power atthe top of the first viewing zone to a second, higher dioptric focalpower at the bottom of the viewing zone, the viewing zone being dividedinto at least three laterally disposed areas; a first one of the threeareas being centrally disposed in the viewing zone, extending verticallytherethrough, and having the principal meridional curve passing throughthe center thereof; the two outermost of the three areas being disposedat the lateral peripheries of the viewing zone and each having a surfaceso curved that the condition δ² f/δxδy = 0 is fulfilled when x and y arethe coordinates in the vertical and horizontal directions respectivelyof said outermost areas and f is the distance of the refractive surfacesfrom the x-y plane whereby skew distortion is so optically compensatedthat at all points on said outermost areas the principal axes ofastigmatism lie in vertical and horizontal planes which are parallel tothe x and y axes respectively to permit a wearer of the lens to perceivehorizontal and vertical lines in the visual environment as beinghorizontal and vertical, and a second viewing zone in verticaljustaposition to the first viewing zone, the second one of the viewingzones having a constant dioptric focal power therethrough, there being adownwardly positive discontinuity in dioptric focal power of less thanabout 0.5 diopters at the boundary between the two viewing zones.
 8. Anophthalmic lens according to claim 7 in which a third viewing zone isdefined on the refractive surface in other vertical juxtaposition to thefirst one of the refractive surface viewing zones, the third viewingzone having a constant dioptric focal power therethrough, the constantdioptric focal power in the third viewing zone being equal to thedioptric focal power at the other juxtaposed end of the range ofdioptric focal power in the first viewing zone.
 9. A progressive powerophthalmic lens according to claim 7 in which the predetermined lawdefines a constant rate of change of dioptric focal power through thefirst viewing zone along the principal meridional curve.
 10. Aprogressive power ophthalmic lens according to claim 7 in which theboundary between the viewing zones being blended so that the boundary isinvisible.
 11. An ophthalmic lens according to claim 7 in which a thirdviewing zone is defined on the refractive surface in other verticaljuxtaposition to the first one of the refractive surface viewing zones,the third viewing zone having a constant dioptric focal powertherethrough, there being a second downwardly positive discontinuity indioptric focal power of less than about 0.5 diopters at the boundarybetween the first and third viewing zones.
 12. A progressive powerophthalmic lens according to claim 11 in which the predetermined lawdefines a constant rate of change of dioptric focal power through thefirst viewing zone along the principal meridional curve.
 13. Aprogressive power ophthalmic lens according to claim 12, in which theboundary between the viewing zones being blended so that the boundary isinvisible.
 14. A progressive power ophthalmic lens according to claim 7,in which the boundary between the viewing zones being blended so thatthe boundary is invisible.